-type f file
-mtime + 7 older than 7 days
-exec rm -f '{}' +
That + at the end was something I found while googling--I'm trying to remember its purpose. Ah, I think it was a way to avoid getting the error of filelist too long.

The + is simply a delimiter to tell find where the -exec command ends. Convenient, because it means that we can avoid a heap of multiple escaping and quoting. (normally, these sort of commands are entered as a single unit, which means quoting with ' or ", escaping with many \\\\'s, or some hellish combination of the three! )

__________________The only dumb question is a question not asked.
The only dumb answer is an answer not given.